Báo cáo toán học: "Degree Sequences of F -Free Graphs" ppsx
Báo cáo toán học: "Degree Sequences of F -Free Graphs" ppsx
... x. For example, for f : x →
x
2
we
have e
f
(F )=e (F ); thus e
f
(F ) can be viewed as a generalization of the size of F .
Define ex
f
(n, F ) to be the maximal value of e
f
(G)overallF -free ... rate of growth of f. For example,
if f grows so fast that e
f
(G) is dominated by the contribution from the vertices of degree
n − 1, then the conclusion of T...
Báo cáo toán học: "Structural Properties of Twin-Free Graphs" doc
... one-twin-free and
connected.
Proof. In this proof, we use twin, twin-free and terminal for one-twin, one-twin-free and
one-terminal, respectively. By Corollary 7, we know that G is not terminal. If ... the
concatenation of the part of P
∗
going from v
1
to v
k
and the part of P
r+1
going from v
k
to x. The length of P is greater than or equal to q + r + 1: there are q edges from v
1
t...
Báo cáo toán học: "The number of F -matchings in almost every tree is a zero residue" ppt
... 92E10
Abstract
For graphs F and G an F -matching in G is a subgraph of G consisting of
pairwise vertex disjoint copies of F . The number of F -match ings in G is denoted
by s (F, G). We show that for every ... if there is one. In fact, this number is the product of the number
of F -ma t chings in every connected component of the forest. By our construction of Z,
at l...
Báo cáo toán học: "the Prism of the Acyclic Orientati" ppsx
... in the other copy of G.
The following lemma, from [1], relates the hamitonicity of prisms and squares for
the electronic journal of combinatorics 2 (1995), #R5 4
Proof: Our proof is by induction ... subgraph of AO(G) × e,namelythat
subgraph induced by all extensions of Γ.
We observe that H can be partitioned into
• [positive pairs] edges of the form [+Γ, +Γ
], and
• [mates] edge...
Báo cáo toán học: "Some properties of unitary Cayley graphs" pdf
... The following lemma will be used to determine the number of common neighbors of a
pair of vertices in X
n
.
Lemma 5. For integers n, s, n ≥ 2, denote by F
n
(s) the number of solutions of the
congruence
x ... journal of combinatorics 14 (2007), #R45 7
2. The multiplicity of zero as an eigenvalue of X
n
is n − m.
3. If α(λ) is the multiplicity of the eigenvalue λ of X
n
,...
Báo cáo toán học: " Degree constrained orientations in countable graphs" pps
... i
G
N
(U). As a u
0
-faulty set is by definition finite,
there is therefore no such set.
Second, let f
1
, f
2
, . . . be an enumeration of the edges of G
0
. Denote the endvertices of
f
1
by x and y, ... satisfy (a)–(c). However, if we agree that v
n
is a neighbour
of itself if there is a loop at v
n
then what follows covers also loops.
For each neighbour w of v
n
in G
n−1
for...
Báo cáo toán học: "A generalization of generalized Paley graphs and new lower bounds for R(3, q)" pot
... choice of a special
element of highest order among the 7 different expressions of S
1
has the advantage of
enhancing the computing efficiency of the clique number of G
n
(A
i
).
3 The computation of ... Science Fund of Guangdong Province (04010384), the Science Fund of Guangxi
Province (0991074, 0991278), the Research Fund of Guangxi Education Committee
(200911LX433), the Res...
Báo cáo toán học: "The Diameter of Almost Eulerian Digraphs" ppsx
... n
i
f
i
= f
i
, so F
i
= f
i
+ f
i+1
+ f
i+2
s since f
i+1
, f
i+2
are non- positive.
If F
i
= s then f
i
= s and so, by s n
i−1
f
i−1
+ n
i
f
i
we conclude that f
i−1
0. Also
f
i+1
= f
i+2
= ... inequalities
s 3f
i
+ f
i+1
and s f
i+1
+ 2f
i+2
.
If f
i+2
2f
i
, then the first inequality leads to s f
i
+ f
i+1
+ f
i+2
. Otherwise 2 f...
Báo cáo toán học: "Independence Complexes of Stable Kneser Graphs" doc
... of ∆, together with a collection o f subsets F ⊆ 2
V
such that
F ∈ F, G ⊆ F ⇒ G ∈ F,
called the faces of ∆. For technical purposes, we include the emptyset as a face. Lov´asz’s
original proof ... vertices for the first of these nodes induce as a subgraph of E
2n+2
a copy of
EL
n−5
while for the second of these nodes the remaining vertices induce a s a subgraph of
E
2n+...